Differentiate
ln(x)
----
..x
x = e?
if so, then
ln(x) / x
= ln(e) / e
= 1/e
And differentiating that will give you zero because 1/e is a constant.
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If you substitute e for x in the derivative dy/dx = {1 -ln(x)} / x^2,
dy/dx = {1 -ln(e)} / e^2
dy/dx = {1 -1} / e^2
dy/dx = {0} / e^2
dy/dx = 0 ------------------still zero.